#
Solution to multiple choice questions: cross-tabulations

These are the solutions to the multiple choice questions as given in *An
Introduction to Medical Statistics, Third Edition. *Section references
are to the book.

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Solution to multiple choice questions 67 to 73: cross-tabulations

67. TFFFF. Section 13.3. 80% of 4 is greater than 3, so all expected frequencies
must exceed 5. The sample size can be as small as 20, if all row and column
totals are 10.
68. FTFTF. Section 13.1, Section 13.3. (5-1) * (3-1) = 8 degrees of
freedom, 80% * 15 = 12 cells must have expected frequencies greater than
5. It is O.K. for an *observed *frequency to be zero.

69. TTFTF. Section 13.1, Section 13.9. The two tests are independent.
There are (2-1) * (2-1) = 1 d.f. With such large numbers Yates' correction
does not make much difference. Without it we get chi-squared = 124.5, with
it we get chi-squared = 119.4 (Section 13.5.).

70. TTTTT. Section 13.4-5. The factorials of large numbers can be difficult
to calculate.

71. TTTTF. Section 13.7. The more closely related the variables are,
the bigger the odds ratio will be. Reversing the order of both rows and
columns turns the *ad/bc *formula to *da/cb*, the same, but reversing
only the columns gives us bc/ad. The ratio of the proportions, or relative
risk, would be *(a/(a+c))/(b/(b+d))*.

72. TTFTT. Chi-squared for trend and Kendall's tau b will both test
the null hypothesis of no trend in the table, but an ordinary chi-squared
test will not (Section 13.8). The odds ratio (OR) is an estimate of the
relative risk for a case-control study (Section 13.7).

73. TTFFF. The test compares proportions in matched samples (Section
13.9). For a relationship, we use the chi-squared test (Section 13.1).
PEFR is a continuous variable, we use the paired t method (Section 10.2).
For two independent samples we use the chi-squared test (Section 13.1).

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Last updated: 17 October, 2003.

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